I can certainly imagine them dropping out, I mean they basically did OTL but there's a big gap between that and switching sides. Also swapping sides leaves them open to a Japanese attack in the pacific. I think the biggest issue is probably the Central Powers not going for it, can St Petersberg really persuade the Turks, Germans and Austrians to suddenly stop killing them and fight alongside them? Can the CP convinced their own people? Can Russia?
I can see one possability... kind of. It's a bit unlikely, but hear me out.
Let's say the Czar's government sends out peace feelers alot earlier: say, Rasputin has a drug-induced "holy vision" and convinces the Czar and Czarinna that they WILL lose their thrones if they don't get out of the war by, say, year's end (Or some other ominious date: let's just say its the end of 1915 for the sake of having just the right balance of CP power, remaining Imperial prestige, and internal Russian stability). While this gets support from certain elements of Russian society, others oppose it: key among them the military leaders who believe they still have a chance. Word leaks to the Entente that the secret talks are taking place, and in response they cut off Russia's credit supply and smuggle in supplies/give the green light for an attempted military coup (Say, led by Krasnov for the sake of simplicity/historical parallels). As a result, there's a split in the country: while the Duma and some of the more moderate liberals don't trust the Czar fully, they want to save their own necks and get a decent peace deal (Plus, having the Czar in their debt and the ultra-conservatives in chains would do wonders for getting their reforms passed), and so back Nicholas, while elements of the military and Pro-Entente ministers (For example, those who make their personal wealth off contracts with French or British firms) continue to fight the CP and wrestle control of Petrograd, Moscow, and other key regions from Imperial Loyalists.
For the sake of making the deal slightly more palatable/realistic, the winter-spring of 1915-1916 sees the Treaty of Belgrade; signed by Germany, A-H, Bulgaria, and The Ottoman Empire on one side and Serbia (Who agree to a negotiated peace following the historical trouncing of their armies) and Imperial Russia on the other, establishing peace on the Eastern Front (Save Salonika). Russian loses are relatively modest; the CP's position not being as strong as it was during B-L, likely limited to Poland, the Baltics, and modest border adjustments in the Caucuses, while Serbia loses Macedonia to Bulgaria, recognizes a pro-Austrian or pro-Ottoman regime in Albania which has rights to Kosovo once they get their civil war under control, and accept a "War Guilt" clause. Krasnov and the military Junta, of course, rejects these terms and tries to set up a competing government. For the sake of arguement, let's say they march into Petrograd while Czar Nicholas is off at the front to welcome the men home from a long war: something that sounds good in the papers and in word of mouth. The Duma is captured and executed or imprisoned; becoming martyers before they can really collect their debt from the Czar, and Krasnov is recognized by the Entente as the legitimate leader of Russia (Or maybe he places a puppet Czar on the throne). Abandoned by their former allies, the Imperial Loyalists sign onto an alliance with Germany: promising to export much-needed grain to A-H and Germany in exchange for arms and military support against the rebellious officers.
Thoughts on this? I imagine the Imperials would be able their Civil War in such a scenario, though "Blue" Russian forces might keep fighting in exile (Say, on the Western Front) even afterwards, in the vein of the Czech Legion